This invention relates to tools for making microcube retroreflective elements for use in manufacturing retroreflective articles, and in particular, retroreflective sheeting; to articles and sheeting having microcubes; and to methods of making such tools and articles; This invention further relates to tools, articles, and methods wherein said microcubes may have boundary shapes other than triangular.
Microcube retroreflective sheeting is now well-known as a material for making reflective highway signs, safety reflectors, reflective vests and other garments, and other safety-related items. Such retroreflective sheeting typically comprises a layer of a clear resin, such as for example, an acrylic or polycarbonate or vinyl, having a smooth front surface and a plurality of retroreflective microcube elements on the reverse surface. Light incident on the smooth front surface passes through the sheeting, impinges on the retroreflective elements, and is reflected back out through the smooth front surface in a direction nominally 180xc2x0 to the direction of incidence.
The reverse surface of the resin layer bearing the microcubes may be further provided with additional layers, such as metallization, which enhances the entrance angularity of the sheeting, or hydrophobic silica, adhesives, release liners, or other layers which otherwise contribute to the functionality of the sheeting.
Cube corner retroreflectors have been used on automobiles and for highway markings since the early 1900""s. These prior art devices were based on macrocube corner elements made by the pin making art. From the use of macrocubes, a number of optical principles involving cube corner technology have been published, and some have been patented. Generally, these principles have involved changes in the size, shape or tilt of the cube faces, or of the included dihedral angles between faces, to achieve desired retroreflector performance. These known optical principles have included:
increasing the efficiency of the retroreflector at large observation angles by changing one or more of the three dihedral angles of the cube, as taught in Heenan U.S. Pat. No. 3,833,285;
increasing the efficiency of the retroreflector at large incident angles by inclining the cube axis with respect to the normal (often called xe2x80x9cangled reflexxe2x80x9d), taught, for example, in Leray patents U.S. Pat. No. 2,055,298 and Br. U.S. Pat. No. 423,464, and in Heenan U.S. Pat. No. 3,332,327;
increasing entrance angularity in one or more planes by including in the array cubes with cube axis cant, as taught in Heenan U.S. Pat. No. 3,873,184 and Heenan U.S. Pat. No. 3,923,378, and, in particular, by positioning one face of each of the oppositely oriented cubes more parallel to the front face of the reflector, as taught in U.S. Heenan et al U.S. Pat. No. 3,541,606 to increase entrance angularity in, two planes at right angles to each other;
increasing uniformity of retroreflectance versus orientation by rotating some cubes by varying degrees about a normal to the front surface of the article, and also by assembling them in arrays of variant dispositions, as in Uding Canadian Pat. No. 785,139; and by angling the cube axis in combination with multiple rotations, as in U.S. Pat. No. 3,923,378.
While these retroreflective optic design principles are well-known in the cube corner art, in more recent years some have attempted to patent them again in microcube sheeting technology, apparently because those persons either did not know what was done in prior macrocube technology, or chose either to ignore or to limit the applicability of the prior art teachings when applied to microcube retroreflective sheeting.
Prior to applicants"" present invention, virtually all microcube sheeting has been limited to the use of microcubes made by ruling along parallel planes. This limitation is a result of the microcube dimensions being smaller than the dimensions obtainable by the cutting, polishing and lapping techniques used in the pin making art. The need to use traditional ruling techniques has inhibited the application of known optical principles to microcubes, and has, with one exception, further generally limited percent active aperture to less than 100%.
The present invention is a major advance in microcube sheeting technology. It enhances both the applicability to microcubes of prior known retroreflective optic principles and the manufacturability of microcubes of different base configurations. Before detailing these advances, further background information is provided.
Retroreflective sheeting and methods of forming the microcube retroreflective elements in such sheeting are disclosed, for example in U.S. Pricone et al. Pat. No. 4,486,363, assigned to the common assignee herein, and incorporated herein by reference in its entirety. As disclosed in such patent, the resinous layer of the sheeting may be on the order of 0.01 inch (0.25 mm) thick or less, and the retroreflective elements formed in the reverse face of the resinous layer comprise triangular microcubes such as are known in the manufacture of flexible retroreflective sheeting
To manufacture such microcube sheeting, generally a master plate of retroreflective triangular microcubes is made by ruling a pattern of retroreflective cube corners into a planar surface of the plate. This is taught generally by Stamm U.S. Pat. No. 3,712,706; is mentioned in U.S. Pat. No. 5,122,902; and is also taught in detail in U.S. Pat. No. 4,478,769, assigned to the applicants"" assignee and incorporated herein by reference in its entirety.
As shown in FIGS. 1A, 2 and 3 of the ""769 patent, the planar surface of a master plate is ruled with a diamond tool which cuts a series of precise parallel V-shaped grooves. To rule equilateral triangular microcubes, three sets of parallel grooves intersecting one another at angles of 60xc2x0 are made; each groove also will have an included angle of substantially 70.53xc2x0, and will be ruled to a groove depth determined by the height of the microcubes desired. This automatically results in an array of oppositely oriented pairs of equilateral triangular microcubes on the face of the master.
The ruled master may then be used to make a series of duplicates, such as by electroforming, and the duplicates are assembled together to form a single xe2x80x9cmotherxe2x80x9d tool. The assembled xe2x80x9cmotherxe2x80x9d tool is used to electroform molds, which are then assembled and ultimately used to form a tool capable of providing the microcube retroreflective elements on the sheeting, such as by embossing, casting, or other means known in the art. A continuous embossing method is disclosed in the aforementioned U.S. Pat. No. 4,478,769; a casting technique for forming microcubes is disclosed, for example, in Rowland U.S. Pat. Nos. 3,684,348 and 3,689,346.
As will be described hereafter, triangular microcubes having bases other than equilateral triangles have been used in an effort to achieve enhanced entrance angularity by use of the well known optical principles taught in macrocube technology. Thus, as taught in applicants"" assignee""s commonly assigned patent Montalbano U.S. Pat. No. 4,633,567, variations of the triangular microcube may be achieved by changing the tool ruling angles (thus, canting the cube axis), thereby adopting and applying some of the prior optical principles to microcube technology. For example, it is possible to achieve arrays having different entrance angularity or orientation angularity (c.f. Rowland U.S. Pat. No. 3,684,348, col. 10, 11. 1-18 and Montalbano U.S. Pat. No. 4,633,567, col. 6, 11. 4-36)
As previously noted, U.S. Pat. No. 3,833,285, discloses that the observation angularity of cube corner retroreflection can be increased in one plane by increasing (or decreasing) one of the three dihedral angles of the cubes; U.S. Pat. Nos. 3,873,184 and 3,923,378, disclose an array of retroreflective elements wherein the cube axes of neighboring cubes are inclined with respect to each other and oppositely oriented such that the entrance angularity is increased; U.S. Pat. No. 3,541,606 discloses that if one cube face of each of the oppositely oriented cubes is xe2x80x9cmore parallelxe2x80x9d to the front surface, entrance angularity is increased in two planes at right angles to each other. Each of the foregoing patents is incorporated herein by reference.
The identical optical principles used in macrocubes for enhancing retroreflectivity have also been applied to the triangular microsized cubes such as are used in retroreflective sheeting. Thus, U.S. Pat. No. 4,588,258 to Hoopman discloses a retroreflective article with purportedly novel wide angularity wherein an array of triangular microcube elements comprises sets of matched pairs with the cube axes of the cubes in each pair being tilted toward one another; but this simply duplicates the face-more-parallel structure disclosed, for example, in applicants"" assignee""s prior U.S. Pat. No. 3,541,606, U.S. Pat. No. 3,923,378 or U.S. Pat. No. 3,873,184 patents. Moreover, the Hoopman matched pairs of triangles are inherent when ruling triangles, which at the time of Hoopman""s application was the only technique used for manufacturing microcubes.
Similarly, U.S. Pat. No. 4,775,219 to Appeldorn, et al., discloses a retroreflective article of modified observation angularity having an array of microcube retroreflective elements formed by three intersecting sets of parallel V-shaped grooves, wherein at least one of the sets includes, in a repeating pattern, at least two groove side angles that differ from one another. The Appeldorn article merely achieves, in an obvious manner, the identical principle taught years ago in applicants"" commonly assigned U.S. Pat. No. 3,833,285.
However, all triangular cubes, while providing adequate retroreflectance, suffer the known disadvantage that inherently by their geometry no more than 66% of their area can be retroreflective for any particular incidence angle. In an attempt to overcome this deficiency of triangular cubes, the Minnesota Mining and Manufacturing Company, in a series of published PCT applications (WO 95/11463; WO 95/11465; WO 95/11467; WO 95/11470), has disclosed arrays of microcubes including some non-triangular cubes, and techniques for ruling such arrays. However, the disclosed arrays have cubes of greatly different heights (which may pose manufacturing problems) and greatly varying aperture size (affecting diffraction and impacting on retroreflectivity). At best, the disclosed arrays provide calculated percent effective aperture (at 0xc2x0 incidence) of 91%, which appears to fall to about 87% when manufacturing draft is considered (see, e.g., WO 95/11470, FIG. 12). If the cubes are canted by the disclosed ruling technique, the efficiency drops even further. The very nature of forming these cubes by intersecting ruled grooves parallel to a single plane inherently limits the results which can be obtained.
The advantages of the techniques and articles of the present invention, as compared to those obtained by the earlier, triangular microcubes or even by the more recent ruled mixtures of triangular and non-triangular cubes, are shown in the drawings of this application and are more specifically described hereinafter.
Unlike triangular cube corners, hexagonal and rectangular cube corners have the advantage that 100% of their area can be retroreflective even at large incidence angles. Also unlike triangular microcubes, however, hexagonal and rectangular microcubes are not defined by continuous straight lines that extend along a planar surface, and therefore cannot be ruled with intersecting sets of parallel lines all parallel to a common plane. Thus, with the sole exception of the rectangular cubes disclosed in U.S. Pat. Nos. 4,349,598 and 4,895,428 (wherein one of the active cube faces is perpendicular to the reflector front surface) it is not possible to cut or rule a master containing all hexagonal or all rectangular microcubes by ruling straight lines in a single flat surface. Moreover, because of the geometric limitations inherent in ruling the cubes for the U.S. Pat. No. 4,349,598 and U.S. Pat. No. 4,895,428 patents, the cube structures disclosed therein are not useful where the primary light source will generally be at a near-zero incidence angle, such as in highway sign sheeting.
Processes for making tools having macrocubes are known in the prior art. Such tools are typically made by assembling a cluster of metal pins, each pin having a single cube corner machined and polished on one end. Hexagonal pins typically may have a dimension across parallel flats on the order of about 0.10 inch (2.5 mm). Rectangular pins have a short dimension of about 0.070 inch (1.8 mm) and a long dimension of about 0.120 inch (3.0 mm). A cluster of such pins is then used as a master to electroform a mold. These larger cubes, because of their height, are too large for use in the manufacture of thin flexible retroreflective sheeting requiring microcubes, but do find utility where larger (and thus taller) retroreflective elements are acceptable, such as in molded plastic reflectors for roadway markers, automobile taillights, and the like.
Because of manufacturing limitations, the smallest pin known to applicants has a cube shape about 0.040xe2x80x3 square. Microcubes as used in flexible retroreflective sheeting generally are no greater than about 0.016 inch (0.4 mm) on a side, and in applicants"" assignee""s commercial sheeting products, the longest edge of the cube shape is about 0.010 inches (0.25 mm).
The term microcube (or a cube of small dimensions), has been used in patents of others to describe or claim sheeting products produced from tools made directly or indirectly from ruled masters, as opposed to retroreflector articles comprising macrocubes typically formed by grouping pins (or by other techniques used to form the larger cubes).
For tooling hexagonal cubes, an alternative to the xe2x80x9cpin clusterxe2x80x9d manufacturing technique is shown in Applied Optics, vol. 20, no. 8, Apr. 15, 1981, pages 296-298. It is there stated that one way to achieve hexagonal cube corners is to accurately machine and polish grooves in the edge surfaces of a stack of flat plates and to assemble the plates at a desired angle. The reference shows a photograph of several flat plates with grooves cut in one edge, stacked one atop the other and with adjacent plates shifted with respect to one another so that the grooves are offset. The tilted stack of plates so assembled results in a set of hexagonal cubes which may be used as a master for electroforming molds. However, this technique was disclosed decades earlier by applicants"" assignee""s founder and was stated to be an unsatisfactory technique for tooling retroreflectors, see U.S. Pat. No. 1,591,572 (FIG. 16, p. 5, 11. 85-99).
Heretoforer, the above-described xe2x80x9cstacked platesxe2x80x9d method of forming macrocubes was not of practical interest for producing molds for retroreflective products on a commercial scale. First, the molds for macrocubes could be made satisfactorily by the aforementioned clustering of hexagonal pins. Secondly, as observed in U.S. Pat. No. 1,591,572, by using conventional machining and polishing techniques, it was not possible to cut and polish inside-intersecting faces with the precise angular tolerances and sharp edges achievable with the pin technique. In particular, any irregularities in the cube surfaces as might be caused by either the cutting operation or the polishing operation could disadvantageously increase the divergence of the retroreflected light and thus diminish the effective retroreflectivity of the cubes so formed. This recognized difficulty in polishing grooved internal angles is highly exacerbated with microcubes because the area that cannot be polished flat is a relatively greater percentage of the resulting cube face area.
As part of the present application, applicants disclose a technique for making and using thin plates that can be ruled without the need of polishing and that can be assembled in various ways to achieve microcube elements not previously available.
It is an object of the present invention to provide an array of microcubes which cannot be produced by ruling in one plane.
It is a further object of the invention to provide an array of microcubes in which the non-dihedral face-edges are not all parallel to a common plane.
It is still another object of the invention to provide means for interrelating three constructional parameters defining a hexagonal microcube (i.e., slippage, groove depth, and plate thickness, explained infra), by which the desired optical characteristics of the microcube can be optimized.
It is still another object of the invention to provide a retroreflective article and, in particular, retroreflective sheeting, having a pattern of hexagonal retroreflective microcubes having desired retroreflective characteristics.
It is another object of the instant invention to provide a method of making a tool including two or more contiguous hexagonal microcubes, which tool can be used for making a retroreflective article and, in particular, retroreflective sheeting.
It is still another object of the invention to provide a method of making a tool having a pattern of all hexagonal microcubes, which tool is made in part by ruling a set of grooves into the ends of a set of plates and then assembling the plates so as to define an array of hexagonal microcubes having desired retroreflective characteristics.
It is yet another object of the invention to provide an article having hexagonal microcubes wherein all of the cube faces are pentagonal; to provide a tool for making such an article; and to provide methods for making such an article and such a tool.
It is yet another object of the invention to provide a retroreflective article and, in particular, retroreflective sheeting, having rectangular retroreflective microcubes in which no dihedral face-edges of one cube are collinear with those of another cube, and in particular, such an article in which the microcubes provide desired retroreflective characteristics.
It is another object of the invention to provide a tool having a unique pattern of rectangular microcubes in which cube axis cant is not constrained by the need for collinearity of dihedral face-edges of adjacent cubes, which tool can be used for making a retroreflective article and, in particular, retroreflective sheeting.
It is another object of the instant invention to provide a method of making a tool having a pattern of rectangular microcubes in which dihedral face-edges are not collinear, which tool can be used for making a retroreflective article having rectangular microcubes, such as sheeting.
It is still another object of the invention to provide a method of making a tool having a pattern of rectangular microcubes, which tool is made in part by ruling grooves and bevels into plate ends to provide a desired rectangular cube shape and pattern.
It is also an object of the invention to provide a method of making rectangular microcube tools by means of assembling flat plates, on one end of which the rectangular microcubes have been formed.
It is still another object of the invention to provide an article having a pattern of retroreflective square microcubes, wherein the microcubes in a square set of four cubes have cube axes canted in four different directions.
It is yet another object of the invention to provide an article having a pattern of retroreflective pentagonal microcubes; to provide a tool for making such an article; and to provide methods for making such an article and such a tool.
It is still another object of the invention to provide an article having a pattern of pentagonal microcubes with canted cube axes, and such an article having pentagonal microcubes with differently canted cube axes, and tools for making such articles and methods for making such tools and articles.
Still a further object of the invention is to provide a retroreflective article having one or more triangular microcubes in which the cube shape and the position of the projection of the cube apex within the cube shape are independent of the cube axis cant.
Yet a further object is to provide such a retroreflective article in which adjacent triangular microcubes may have different degrees of inclination of the cube axes and are not necessarily matched pairs.
Other objects, advantages, and novel features of the instant invention will be understood by those skilled in the art from the following specification and the drawings appended hereto.
In accordance with the invention, methods are disclosed for making a tool having a pattern of microcubes for use in making a retroreflective article. A plurality of plates is provided, each plate having two substantially parallel planar surfaces and at least one end made of a material that can be cut by a cutting tool that will produce an optical surface, as cut. The plate has a micro-sized thickness xe2x80x9ctxe2x80x9d, i.e., on the order of about one or two microcube widths, depending upon the type of microcube-corner to be tooled. The thickness need not be the same for all plates.
Many shapes of microcubes are manufacturable using the plate process disclosed herein. Two shapes, hexagonal and rectangular, are discussed in detail; other shapes are described more generally to illustrate the versatility of the process.
Hexagonal Microcubes
To produce a pattern of hexagonal microcubes, the plates are stacked one against another so that the set of ends of cuttable material lies substantially in a single plane, which, in a preferred form, is substantially perpendicular to the parallel planar surfaces of each plate. A series of parallel V-shaped grooves is ruled with a cutting tool into the set of cuttable ends. The ruled grooves preferably have polished surfaces as cut and therefore do not require subsequent lapping and polishing as do pins used in making macrocubes.
In one embodiment of the invention, the direction of cutting the grooves is nominally perpendicular to the planar surfaces of the plates, the length xe2x80x9cLxe2x80x9d of each inclined surface of the groove perpendicular to the direction of cutting is chosen to be equal to the thickness xe2x80x9ctxe2x80x9d of the plate, and the included angle between the inclined surfaces is about 90xc2x0, the included angle may be varied from 90xc2x0 by tilting the cutting face of the cutting tool with respect to the surface being cut.
The grooved plates are then offset from one another by half a groove width horizontally and possibly, but not necessarily, by the depth xe2x80x9cdxe2x80x9d of one groove vertically, so that the top edge of a groove in one plate coincides with the bottom edge of a ruled groove in the adjacent plate, thus creating two superimposed arrays of hexagonal cube corners. One array consists of female (concave) hexagonal cube corners, each comprised of the exposed planar surface of one plate plus the two surfaces of one groove of the next adjacent plate. The other array consists of male (convex) hexagonal cube corners, each comprised of the exposed planar surface of one plate plus two adjacent surfaces from adjacent grooves in that same plate. For greater accuracy in the eventual retroreflective article, the male cube corners are preferred, because they avoid any plate-to-plate angular errors.
Rectangular Microcubes
To produce a pattern of rectangular microcubes, in one embodiment, plates of a chosen thickness xe2x80x9ctxe2x80x9d are stacked alternately with slightly shorter spacers. The assembly of plates and spacers is tilted at a predetermined preferred angle, with one set of edges of the cuttable ends lying in a plane parallel to the bed of the ruling machine. The cuttable end of each plate is then bevel cut by means of a cutting tool so that the beveled face is perpendicular to the bed of the ruling machine. A series of grooves of desired included angle is then cut by the cutting tool in a direction substantially perpendicular to the beveled face. To create an electroforming master comprising rectangular microcubes, the spacers are removed and the plates are then stacked together with adjoining plates rotated 180xc2x0 with respect to each other with the apices of the rectangular cube-corners all lying in the same plane perpendicular to the plane of the sides of the plates and with the apices of cubes in adjoining plates aligned parallel to the grooves.
Manufacture of Article
The stack of grooved plates (for hexagonal cubes) or grooved and beveled plates (for rectangular cubes) may then be used as a master for electroforming a mold insert or for initiating a mothering process to electroform a larger mold insert or an embossing belt, as shown in patent U.S. Pat. No. 4,478,769 for the manufacture of retroreflective articles and, in particular, retroreflective sheeting, but now having a pattern of hexagonal or rectangular microcubes. The use of hexagonal or rectangular microcubes instead of triangular microcubes advantageously increases the active aperture of the article as projected parallel to the principal refracted ray from 66% or less to essentially 100%.
For purposes of this application, Applicants are using certain terms in a particular sense, as defined herein, and other terms in accordance with industry accepted practice, such as current ASTM definitions. Note that many of these definitions distinguish between a cube and a cube shape, each of which is defined herein.
Adjacentxe2x80x94for microcubes, having a portion of an edge of the shape of one cube essentially coincident with a portion of an edge of the shape of another cube.
Angle of incidencexe2x80x94the angle between the illumination axis and the normal to the front surface of a retroreflector. See also xe2x80x9centrance angle.xe2x80x9d
Array active aperturexe2x80x94the sum of the active apertures of the individual microcube elements making up the array. (See also xe2x80x9cpercent active aperturexe2x80x9d)
Contiguous microcubesxe2x80x94microcubes, a non-dihedral face-edge of one of which is coincident with a non-dihedral face-edge of another microcube. Compare, xe2x80x9cadjacent cubes.xe2x80x9d Note that non-contiguous microcubes may be adjacent. An array of contiguous microcubes is one in which the non-dihedral face edges of each microcube (except those at the perimeter of the array) are concident with non-dihedral face edges of another microcube.
Cube (also xe2x80x9ccube cornerxe2x80x9d)xe2x80x94an element consisting of three nominally perpendicular faces, regardless of the size or shape of the faces; often referred to in industry and literature as xe2x80x9ccorner cubesxe2x80x9d, xe2x80x9ctrihedralsxe2x80x9d or xe2x80x9ctetrahedronsxe2x80x9d.
Cube areaxe2x80x94the area enclosed by the cube shape.
Cube axisxe2x80x94a central axis that is the trisector of the internal space defined by the three intersecting faces of a microcube. In the art, sometimes called the xe2x80x9csymmetry axis.xe2x80x9d
Cube axis cantxe2x80x94the angle between the cube axis and the principal refracted ray. The sign of the cant is negative for face-more-parallel and positive for edge-more-parallel. A cube is considered canted when the cube axis cant is not zero.
Cube diagonalxe2x80x94for certain cube corners, an imaginary line passing through the apex of the cube corner at an angle such that in a projection of the outline of the cube corner parallel to the cube diagonal, every line through the apex terminating on both ends at the cube shape will be bisected by the apex.
Cube perimeterxe2x80x94closed spatial curve comprising the non-dihedral edges of the faces of a cube. In instances where there is an uninterrupted surface shared by two or more microcubes, the dividing lines between microcubes shall be considered to be the shortest lines that can be drawn to complete the polygon (see e.g. FIG. 27B).
Cube shapexe2x80x94the two-dimensional geometrical figure defined by the projection of the cube perimeter in the direction of the principal refracted ray. Thus, a triangular cube has a cube shape that is a triangle, a hexagonal cube has a cube shape that is a hexagon, and so forth.
Cube symmetry planexe2x80x94a plane that divides a cube corner into mirror images. Not all cube corners have a plane of symmetry.
Design rayxe2x80x94an imaginary line through the cube apex in a tool, which ray is coincident with the principal refracted ray in the article.
Dihedral face-edgexe2x80x94intersection of two faces of a single cube.
Entrance anglexe2x80x94the angle between the illumination axis and the optical axis (retroreflector axis). Note the distinction between entrance angle and angle of incidence. The angle of incidence is always measured between the incident ray and the normal to the surface (which may or may not be the retroreflector axis), whereas the entrance angle is measured between the incident ray and the retroreflector axis (which may or may not be the normal to the surface). Entrance angle is a measure only of the amount by which an incident ray is angled to the retroreflector axis, and is not concerned with the normal; angle of incidence is a measure only of the amount by which an incident ray is angled to the normal, and is not concerned with the retroreflector axis. For example, a pavement marker may be designed for the normal to the marker surface to be angled 60xc2x0 to the optical axis; if light from an approaching vehicle is incident upon that marker along the retroreflector axis, the entrance angle is 0xc2x0 and the angle of incidence is 60xc2x0, if light from an approaching vehicle is incident on the marker at a horizontal angle of 20xc2x0 with respect to the retroreflector axis, the entrance angle is 20xc2x0 and the angle of incidence is 61.98xc2x0=[cosxe2x88x921(cos 60)(cos 20)].
xe2x80x9cFace-more-parallelxe2x80x9d and xe2x80x9cedge-more-parallelxe2x80x9d refer to the positioning of the cube relative to the principal refracted ray. When the angles between the cube faces and the principal refracted ray are not all equal to 35.26xc2x0, the cube is xe2x80x9cface-more-parallelxe2x80x9d or xe2x80x9cedge-more-parallelxe2x80x9d depending upon whether the face angle with respect to the principal refracted ray that is most different from 35.26xc2x0 is respectively greater or less than 35.26xc2x0. In the case of sheeting or other retroreflectors for which the principal refracted ray is nominally perpendicular to the front surface of the retroreflector, then for face-more-parallel microcubes the selected cube face will also be more parallel to the reflector front surface than will any face of an uncanted microcube.
Horizontal entrance anglexe2x80x94for pavement markers, the angle in the horizontal plane between the direction of incident light and the retroreflector axis.
Incidence anglexe2x80x94see, xe2x80x9cangle of incidence.xe2x80x9d
Microcube (also xe2x80x9cmicrocube cornerxe2x80x9d)xe2x80x94a cube corner having a maximum area of about 0.0016 square inches (1 mm2).
Non-dihedral face-edgexe2x80x94edge of a microcube face that is not a dihedral face-edge, i.e., an edge that is a segment of the cube perimeter.
Optical axisxe2x80x94a designated line segment from the retroreflector center that is chosen centrally among the intended directions of illumination, such as the direction of the road on which or with respect to which the retroreflector is intended to be mounted.
Pairedxe2x80x94oppositely oriented. Paired cubes, as used herein, refers to oppositely oriented adjacent cubes. Paired arrays, as used herein, refers to two arrays, the cubes in one array being oppositely oriented to the cubes of the other.
Percent active aperturexe2x80x94that portion of the projected area of an array that is retroreflectively functional for a particular selected direction of projection. (This definition assumes that the rear surfaces of the cube are 100% reflective. This definition is equivalent to that used in WO 95/11470, page 6, lines 23-25.)
Principal incident rayxe2x80x94a light ray parallel to the optical axis, chosen so that after refraction at the article""s front surface, the ray passes through the apex of the cube corner.
Principal refracted rayxe2x80x94the continuation of the principal incident ray after refraction at the retroreflector front surface.
Retroreflectancexe2x80x94the product of percent active aperture times each cube face""s reflectivity times the square of the transmission (to account for Fresnel transmission loss) of the front surface. (This term differs from xe2x80x9ctotal light returnxe2x80x9d as defined in WO95/11467, page 17, lines 26 and 27, by inclusion in xe2x80x9cretroreflectancexe2x80x9d of the Fresnel loss of the front surface.) Photometrically, retroreflectance is the measure of the total retroreflection accumulated over all appropriately small observation angles and all rotation angles.
Retroreflector axisxe2x80x94same as xe2x80x9coptical axis.xe2x80x9d
Rulablexe2x80x94capable of being generated by the repeated straight-line motion of a shaped tool along paths parallel to a common plane.
Zone of reflectorizationxe2x80x94the range of entrance angles in a given entrance plane throughout which the retroreflector maintains a given minimum retroreflectance.